Solutions to the optimal prediction problem (REF ) and the optimal prescription problem (REF ) will come to depend heavily on the choice of the strength of the imposed out-of-sample performance via the choice of the sequence \((a_T)_{T\ge 1}\) . The larger \((a_T)_{T\ge 1}\) , the stronger the required guarantees and consequently the more conservative the feasible predictors and prescriptors. Perhaps surprisingly, in each scenario of the out-of-sample guarantee, there exists a strongly optimal solution which we can exhibit. To prove this result we will assume in this paper that the set of events \(\Sigma \)  has finite cardinality. Extending our results to the more general case of continuous event sets, along the lines of [1]}, is a possibility but would require a vastly more technical exposition. We believe that the results in the discrete event case which we present momentarily are sufficiently interesting to warrant this slightly restrictive assumption.
